Global Optimization of Nonlinear Blend-Scheduling Problems

The scheduling of gasoline-blending operations is an important problem in the oil refining industry. Thisproblem not only exhibits the combinatorial nature that is intrinsic to scheduling problems, but alsonon-convex nonlinear behavior, due to the blending of various materials with different quality properties.In this work, a global optimization algorithm is proposed to solve a previously published continuous-timemixed-integer nonlinear scheduling model for gasoline blending. The model includes blend recipe optimi-zation, the distribution problem, and several important operational features and constraints. The algorithmemploys piecewise McCormick relaxation （PMCR） and normalized multiparametric disaggregation tech-nique （NMDT） to compute estimates of the global optimum. These techniques partition the domain of oneof the variables in a bilinear term and generate convex relaxations for each partition. By increasing the num-ber of partitions and reducing the domain of the variables, the algorithm is able to refine the estimates ofthe global solution. The algorithm is compared to two commercial global solvers and two heuristic methodsby solving four examples from the literature. Results show that the proposed global optimization algorithmperforms on par with commercial solvers but is not as fast as heuristic approaches.

Global Optimization Algorithm for Nonlinear Sum of Ratios Problems

In this paper, a global optimization algorithm is proposed for nonlinear sum of ratios problem （P）. The algorithm works by globally solving problem （P1） that is equivalent to problem （P）, by utilizing linearization technique a linear relaxation programming of the （P1） is then obtained. The proposed algorithm is convergent to the global minimum of （P1） through the successive refinement of linear relaxation of the feasible region of objective function and solutions of a series of linear relaxation programming. Numerical results indicate that the proposed algorithm is feasible and can be used to globally solve nonlinear sum of ratios problems （P）.

Global optimization over linear constraint non-convex programming problem

A improving Steady State Genetic Algorithm for global optimization over linear constraint non-convex programming problem is presented. By convex analyzing, the primal optimal problem can be converted to an equivalent problem, in which only the information of convex extremes of feasible space is included, and is more easy for GAs to solve. For avoiding invalid genetic operators, a redesigned convex crossover operator is also performed in evolving. As a integrality, the quality of two problem is proven, and a method is also given to get all extremes in linear constraint space. Simulation result show that new algorithm not only converges faster, but also can maintain an diversity population, and can get the global optimum of test problem.

Global Optimization for Solving Linear Non-Quadratic Optimal Control Problems

This paper presents a global optimization approach to solving linear non-quadratic optimal control problems. The main work is to construct a differential flow for finding a global minimizer of the Hamiltonian function over a Euclid space. With the Pontryagin principle, the optimal control is characterized by a function of the adjoint variable and is obtained by solving a Hamiltonian differential boundary value problem. For computing an optimal control, an algorithm for numerical practice is given with the description of an example.

Seismic displacement demand prediction in non-linear domain: Optimization of the N2 method

In Europe, computation of displacement demand for seismic assessment of existing buildings is essentially based on a simplified formulation of the N2 method as prescribed by Eurocode 8(EC8). However, a lack of accuracy of the N2 method in certain conditions has been pointed out by several studies. This paper addresses the assessment of effectiveness of the N2 method in seismic displacement demand determination in non-linear domain. The objective of this work is to investigate the accuracy of the N2 method through comparison with displacement demands computed using non-linear timehistory analysis(NLTHA). Results show that the original N2 method may lead to overestimation or underestimation of displacement demand predictions. This may affect results of mechanical model-based assessment of seismic vulnerability at an urban scale. Hence, the second part of this paper addresses an improvement of the N2 method formula by empirical evaluation of NLTHA results based on EC8 ground-classes. This task is formulated as a mathematical programming problem in which coefficients are obtained by minimizing the overall discrepancy between NLTHA and modified formula results. Various settings of the mathematical programming problem have been solved using a global optimization metaheuristic. An extensive comparison between the original N2 method formulation and optimized formulae highlights benefits of the strategy.

Global robust optimal sliding mode control for uncertain affine nonlinear systems

The problem of robustifying linear quadratic regulators （LQRs） for a class of uncertain affine nonlinear systems is considered. First, the exact linearization technique is used to transform an uncertain nonlinear system into a linear one and an optimal LQR is designed for the corresponding nominal system. Then, based on the integral sliding mode, a design approach to robustifying the optimal regulator is studied. As a result, the system exhibits global robustness to uncertainties and the ideal sliding mode dynamics is the same as that of the optimal LQR for the nominal system. A global robust optimal sliding mode control （GROSMC） is realized. Finally, a numerical simulation is demonstrated to show the effectiveness and superiority of the proposed algorithm compared with the conventional optimal LQR.

An Overview of Sequential Approximation in Topology Optimization of Continuum Structure

This paper offers an extensive overview of the utilization of sequential approximate optimization approaches in the context of numerically simulated large-scale continuum structures.These structures,commonly encountered in engineering applications,often involve complex objective and constraint functions that cannot be readily expressed as explicit functions of the design variables.As a result,sequential approximation techniques have emerged as the preferred strategy for addressing a wide array of topology optimization challenges.Over the past several decades,topology optimization methods have been advanced remarkably and successfully applied to solve engineering problems incorporating diverse physical backgrounds.In comparison to the large-scale equation solution,sensitivity analysis,graphics post-processing,etc.,the progress of the sequential approximation functions and their corresponding optimizersmake sluggish progress.Researchers,particularly novices,pay special attention to their difficulties with a particular problem.Thus,this paper provides an overview of sequential approximation functions,related literature on topology optimization methods,and their applications.Starting from optimality criteria and sequential linear programming,the other sequential approximate optimizations are introduced by employing Taylor expansion and intervening variables.In addition,recent advancements have led to the emergence of approaches such as Augmented Lagrange,sequential approximate integer,and non-gradient approximation are also introduced.By highlighting real-world applications and case studies,the paper not only demonstrates the practical relevance of these methods but also underscores the need for continued exploration in this area.Furthermore,to provide a comprehensive overview,this paper offers several novel developments that aim to illuminate potential directions for future research.

Least Squares Solution for Discrete Time Nonlinear Stochastic Optimal Control Problem with Model-Reality Differences

In this paper, an efficient computational approach is proposed to solve the discrete time nonlinear stochastic optimal control problem. For this purpose, a linear quadratic regulator model, which is a linear dynamical system with the quadratic criterion cost function, is employed. In our approach, the model-based optimal control problem is reformulated into the input-output equations. In this way, the Hankel matrix and the observability matrix are constructed. Further, the sum squares of output error is defined. In these point of views, the least squares optimization problem is introduced, so as the differences between the real output and the model output could be calculated. Applying the first-order derivative to the sum squares of output error, the necessary condition is then derived. After some algebraic manipulations, the optimal control law is produced. By substituting this control policy into the input-output equations, the model output is updated iteratively. For illustration, an example of the direct current and alternating current converter problem is studied. As a result, the model output trajectory of the least squares solution is close to the real output with the smallest sum squares of output error. In conclusion, the efficiency and the accuracy of the approach proposed are highly presented.

A Primal-Dual SGD Algorithm for Distributed Nonconvex Optimization

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of n local cost functions by using local information exchange is considered.This problem is an important component of many machine learning techniques with data parallelism,such as deep learning and federated learning.We propose a distributed primal-dual stochastic gradient descent(SGD)algorithm,suitable for arbitrarily connected communication networks and any smooth(possibly nonconvex)cost functions.We show that the proposed algorithm achieves the linear speedup convergence rate O(1/(√nT))for general nonconvex cost functions and the linear speedup convergence rate O(1/(nT)) when the global cost function satisfies the Polyak-Lojasiewicz(P-L)condition,where T is the total number of iterations.We also show that the output of the proposed algorithm with constant parameters linearly converges to a neighborhood of a global optimum.We demonstrate through numerical experiments the efficiency of our algorithm in comparison with the baseline centralized SGD and recently proposed distributed SGD algorithms.

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

System-L evel Efficiency Optimization of a Linear Induction Motor Drive System

Linear induction motors are superior to rotary induction motors in direct drive systems because they can generate direct forward thrust force independent of mechanical transmission.However,due to the large air gap and cut-open magnetic circuit,their efficiency and power factor are quite low,which limit their application in high power drive systems.To attempt this challenge,this work presents a system-level optimization method for a single-sided linear induction motor drive system.Not only the motor but also the control system is included in the analysis.A system-level optimization method is employed to gain optimal steady-state and dynamic performances.To validate the effectiveness of the proposed optimization method,experimental results on a linear induction motor drive are presented and discussed.

A self-adaptive linear evolutionary algorithm for solving constrained optimization problems

In many real-world applications of evolutionary algorithms,the fitness of an individual requires a quantitative measure.This paper proposes a self-adaptive linear evolutionary algorithm （ALEA） in which we introduce a novel strategy for evaluating individual＇s relative strengths and weaknesses.Based on this strategy,searching space of constrained optimization problems with high dimensions for design variables is compressed into two-dimensional performance space in which it is possible to quickly identify ＇good＇ individuals of the performance for a multiobjective optimization application,regardless of original space complexity.This is considered as our main contribution.In addition,the proposed new evolutionary algorithm combines two basic operators with modification in reproduction phase,namely,crossover and mutation.Simulation results over a comprehensive set of benchmark functions show that the proposed strategy is feasible and effective,and provides good performance in terms of uniformity and diversity of solutions.

A LINEAR PRECODING STRATEGY BASED ON PARTICLE SWARM OPTIMIZATION IN MULTICELL COOPERATIVE TRANSMISSION

An optimal linear precoding scheme based on Particle Swarm Optimization(PSO),which aims to maximize the system capacity of the cooperative transmission in the downlink channel,is proposed for a multicell multiuser single input single output system.With such a scheme,the optimal precoding vector could be easily searched for each user according to a simplified objective function.Simulation results show that the proposed scheme can obtain larger average spectrum efficiency and a better Bit Error Rate(BER) performance than Zero Forcing(ZF) and Minimum Mean Square Error(MMSE) algorithm.

Stabilization of linear time-varying systems with state and input constraints using convex optimization

The stabilization problem of linear time-varying systems with both state and input constraints is considered. Sufficient conditions for the existence of the solution to this problem are derived and a gain-switched（gain-scheduled） state feedback control scheme is built to stabilize the constrained timevarying system. The design problem is transformed to a series of convex feasibility problems which can be solved efficiently. A design example is given to illustrate the effect of the proposed algorithm.

Fuzzy linear model for production optimization of mining systems with multiple entities

Planning and production optimization within multiple mines or several work sites （entities） mining systems by using fuzzy linear programming （LP） was studied. LP is the most commonly used operations research methods in mining engineering. After the introductory review of properties and limitations of applying LP, short reviews of the general settings of deterministic and fuzzy LP models are presented. With the purpose of comparative analysis, the application of both LP models is presented using the example of the Bauxite Basin Niksic with five mines. After the assessment, LP is an efficient mathematical modeling tool in production planning and solving many other single-criteria optimization problems of mining engineering. After the comparison of advantages and deficiencies of both deterministic and fuzzy LP models, the conclusion presents benefits of the fuzzy LP model but is also stating that seeking the optimal plan of production means to accomplish the overall analysis that will encompass the LP model approaches.

Improved non-dominated sorting genetic algorithm (NSGA)-II in multi-objective optimization studies of wind turbine blades

The non-dominated sorting genetic algorithm （NSGA） is improved with the controlled elitism and dynamic crowding distance. A novel multi-objective optimization algorithm is obtained for wind turbine blades. As an example, a 5 MW wind turbine blade design is presented by taking the maximum power coefficient and the minimum blade mass as the optimization objectives. The optimal results show that this algorithm has good performance in handling the multi-objective optimization of wind turbines, and it gives a Pareto-optimal solution set rather than the optimum solutions to the conventional multi objective optimization problems. The wind turbine blade optimization method presented in this paper provides a new and general algorithm for the multi-objective optimization of wind turbines.

Optimization Algorithms for Sidelobes SSL Reduction: A Comparative Study

The development of new technologies in smart cities is often hailed as it becomes a necessity to solve many problems like energy consumption and transportation. Wireless networks are part of these technologies but implementation of several antennas, using different frequency bandwidths for many applications might introduce a negative effect on human health security. In wireless networks, most antennas generate sidelobes SSL. SSL causes interference and can be an additional resource for RF power that can affect human being health. This paper aims to study algorithms that can reduce SSL. The study concerns typical uniform linear antenna arrays. Different optimum side lobe level reduction algorithms are presented. Genetic algorithm GA, Chebyshev, and Particle Swarm Optimization algorithm are used in the optimization process. A comparative study between the indicated algorithms in terms of stability, precision, and running time is shown. Results show that using these algorithms in optimizing antenna parameters can reduce SSL. A comparison of these algorithms is carried out and results show the difference between them in terms of running time and SSL reduction Level.

Reliability-based Robust Optimization Design of Automobile Components with Non-normal Distribution Parameters

In the reliability designing procedure of the vehicle components, when the distribution styles of the random variables are unknown or non-normal distribution, the result evaluated contains great error or even is wrong if the reliability value R is larger than 1 by using the existent method, in which case the formula is necessary to be revised. This is obviously inconvenient for programming. Combining reliability-based optimization theory, robust designing method and reliability based sensitivity analysis, a new method for reliability robust designing is proposed. Therefore the influence level of the designing parameters’ changing to the reliability of vehicle components can be obtained. The reliability sensitivity with respect to design parameters is viewed as a sub-objective function in the multi-objective optimization problem satisfying reliability constraints. Given the first four moments of basic random variables, a fourth-moment technique and the proposed optimization procedure can obtain reliability-based robust design of automobile components with non-normal distribution parameters accurately and quickly. By using the proposed method, the distribution style of the random parameters is relaxed. Therefore it is much closer to the actual reliability problems. The numerical examples indicate the following: (1) The reliability value obtained by the robust method proposed increases (】0.04%) comparing to the value obtained by the ordinary optimization algorithm; (2) The absolute value of reliability-based sensitivity decreases (】0.01%), and the robustness of the products’ quality is improved accordingly. Utilizing the reliability-based optimization and robust design method in the reliability designing procedure reduces the manufacture cost and provides the theoretical basis for the reliability and robust design of the vehicle components.

Non-derivative solution to nonlinear dynamic optimal design of class two for deformation network monitoring

Based on the nonlinear error equation of deformation network monitoring, the mathematical model of nonlinear dynamic optimal design of class two was put forward for the deformation network monitoring, in which the target function is the accuracy criterion and the constraint conditions are the network’s sensitivity, reliability and observing cost. Meanwhile a new non derivative solution to the nonlinear dynamic optimal design of class two was also put forward. The solving model uses the difference to stand for the first derivative of functions and solves the revised feasible direction to get the optimal solution to unknown parameters. It can not only make the solution to converge on the minimum point of the constraint problem, but decrease the calculating load.